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Neural Network Modelling and Dynamical System Theory

Are They Relevant to Study the Governing Dynamics of Association Football Players?


Recent studies have explored the organization of player movements in team sports using a range of statistical tools. However, the factors that best explain the performance of association football teams remain elusive. Arguably, this is due to the high-dimensional behavioural outputs that illustrate the complex, evolving configurations typical of team games. According to dynamical system analysts, movement patterns in team sports exhibit nonlinear self-organizing features. Nonlinear processing tools (i.e. Artificial Neural Networks; ANNs) are becoming increasingly popular to investigate the coordination of participants in sports competitions. ANNs are well suited to describing high-dimensional data sets with nonlinear attributes, however, limited information concerning the processes required to apply ANNs exists. This review investigates the relative value of various ANN learning approaches used in sports performance analysis of team sports focusing on potential applications for association football. Sixty-two research sources were summarized and reviewed from electronic literature search engines such as SPORTDiscus™, Google Scholar, IEEE Xplore, Scirus, ScienceDirect and Elsevier. Typical ANN learning algorithms can be adapted to perform pattern recognition and pattern classification. Particularly, dimensionality reduction by a Kohonen feature map (KFM) can compress chaotic high-dimensional datasets into low-dimensional relevant information. Such information would be useful for developing effective training drills that should enhance self-organizing coordination among players. We conclude that ANN-based qualitative analysis is a promising approach to understand the dynamical attributes of association football players.

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  1. 1.

    Glazier PS. Game, set and match? Substantive issues and future directions in performance analysis. Sports Med 2010; 40 (8): 625–34

  2. 2.

    Barris S, Button C. A review of vision-based motion analysis in sport. Sports Med 2008; 38 (12): 1025–43

  3. 3.

    Wilson GE. A framework for teaching tactical game knowledge. J Physical Edu Rec Dance 2002; 73 (1): 20–6

  4. 4.

    Wallace SA. Dynamic pattern perspective of rhythmic movement: an introduction. In: Zelaznik HN, editor. Advances in motor learning and control. Champaign (IL): Human Kinetics, 1996

  5. 5.

    Clark JE. On becoming skillful: patterns and constraints. Res Q Exercise Sport 1995; 66: 173–83

  6. 6.

    Kugler PN. A morphological perspective on the origin and evolution ofmovement patterns. In:Wade MG, Whiting HTA, editors. Motor development in children: aspects of coordination and control. Dordrecht: Martinus Nijhoff, 1986: 459–525

  7. 7.

    Cooke NJ, Cannon-Bowers JA, Stout RJ. Measuring team knowledge. Hum Factors 2000; 42: 151–73

  8. 8.

    Kauffman S. The origins of order: self organization and selection in evolution. New York: Oxford University Press, 1993

  9. 9.

    Kelso JA. Dynamic patterns: the self-organization of brain and behavior. Cambridge (MA): MIT Press, 1995

  10. 10.

    Davids K, Button C, Bennett S. Dynamics of skill acquisition: a constraints-led approach. Champaign (IL): Human Kinetics, 2008

  11. 11.

    Kugler PN, Kelso JAS, Turvey MT. On the control and coordination of naturally developing systems. In: Kelso JAS, Clark E, editors. The development of movement control and coordination. New York: Wiley, 1982

  12. 12.

    Bernstein N. The coordination and regulation of movement. New York: Pergamon, 1967

  13. 13.

    Kelso JAS. Contrasting perspectives on order and regulation in movement. In: Long J, Baddeley A, editors. Attention and performance IX. Mahwah (NJ): Lawrence Erlbaum Associates, 1981: 437–57

  14. 14.

    Iberall AS, Soodak H. Physical basis for complex: some propositions relating levels of organisation. Collective Phenomena 1978; 3: 9–24

  15. 15.

    Prigogine I, George C, Hennin F, et al. A unified formulation of dynamics and thermodynamics. Chem Scr 1973; 4: 5–32

  16. 16.

    Davids K, Glazier P, Araújo D, et al. Movement systems as dynamical systems: the functional role of variability and its implications for sportsmedicine. Sports Med 2003; 3: 245–60

  17. 17.

    Davids K, Araújo D, Shuttleworth R. Applications of dynamical systems theory to football. In: Cabri J, Reilly T, Araújo D, editors. Science and football V. London: Routledge, 2005

  18. 18.

    McGarry T, Anderson DI, Wallace SA, et al. Sport competition as a dynamical self-organizing system. J Sports Sci 2002; 20: 771–81

  19. 19.

    Bourbousson J, Seve C, McGarry T. Space-time coordination dynamics in basketball: part 2. The interaction between two teams J Sports Sci 28 (3): 349–58

  20. 20.

    Hristovski R, Davids K, Araújo D, et al. How boxers decide to punch a target: emergent behaviour in nonlinear dynamical movement systems. J Sports Sci Med 2006; 5 (CSSI): 60–73

  21. 21.

    Passos P, Araújo D, Davids K, et al. Information-governing dynamics of attacker-defender interactions in youth rugby union. J Sports Sci 2008; 26 (13): 1421–9

  22. 22.

    McGarry T, Franks IM. In search of invariant athletic behaviour in competitive sport systems: an example from championship squash match-play. J Sports Sci 1996; 14: 445–56

  23. 23.

    Palut Y, Zanone PG. A dynamical analysis of tennis: concepts and data. J Sports Sci 2005; 23: 1021–32

  24. 24.

    Beek PJ, Beek WJ. Tools for constructing dynamical models of rhythmic movement. Hum Mov Sci 1988; 7: 301–42

  25. 25.

    Passos P, Davids K, Araújo K, et al. Networks as novel tool for studying team ball sports as complex social systems. J Sci Med Sport 2011; 14 (2): 170–6

  26. 26.

    Passos P, Araújo D, Davids K, et al. Interpersonal pattern dynamics and adaptive behaviour in multiagent neurobiological systems: conceptual model and data. J Motor Behav 2009; 41 (5): 445–59

  27. 27.

    Frencken WGP, Lemmink KAPM. Team kinematics of small-sided soccer games: a systematic approach. In: Reill T, Korkusuz F, editors. Science and football VI: proceedings of the 6th World Congress on Science and Football. London: Routledge, 2008: 161–6

  28. 28.

    Grehaigne JF, Boutheir D, Bernard D. Dynamic-system analysis of opponent relationships in collective actions of soccer. J Sports Sci 1997; 15: 137–49

  29. 29.

    Bourbousson J, Seve C, McGarry T. Space-time coordination dynamics in basketball: part 1. Intra- and intercouplings among player dyads J Sports Sci 28 (3): 339–47

  30. 30.

    McGarry T, Khan MA, Franks IM. On the presence and absence of behavioral traits in sport: an example from championship squash match-play. J Sports Sci 1999; 17: 297–311

  31. 31.

    McGarry T. Applied and theoretical perspectives of performance analysis in sport: scientific issues and challenges. Int J Perform Anal Sport 2009; 9: 128–40

  32. 32.

    Lames M. Modelling the interaction in game sports: relative phase and moving correlations. J Sports Sci Med 2006; 5: 556–60

  33. 33.

    Players Heat Map. 2010 FIFA World Cup South Africa® [online]. Available from URL: http://www.fifa.com/search/index.html?q=heat+map [Accessed 2011 Mar 29]

  34. 34.

    Stergiou N, Buzzi UH, Kurz MJ, et al. Nonlinear tools in human movement. In: Stergiou N, editor. Innovative analysis of human movement. Champaign (IL): Human Kinetics, 2004: 66–77

  35. 35.

    Haykin S. Neural networks: a comprehensive foundation. 2nd ed. Upper Saddle River (NJ): Prentice-Hall Inc., 1999

  36. 36.

    Benuskov’a L, Diamond ME, Ebner FF. Dynamic synaptic modification threshold: computational model of experience dependent plasticity in adult rat barrel cortex. Proc Natl Acad Sci U S A 1994; 91: 4791–5

  37. 37.

    Maass W. Networks of spiking neurons: the third generation of neural network models. Neural Networks 1997; 10 (9): 1659–71

  38. 38.

    Kimoto T, Asakawa K, Yoda M, et al. Stock market prediction system with modular neural networks. In: Trippi RR, Turban E, editors. Neural networks in finance and investing. Chicago (IL): Probus Publishing Co., 1994: 343–57

  39. 39.

    Zhang G, Patuwo BE, Hu MY. Forecasting with artificial neural networks: the state of the art. Int J Forecasting 1998; 14: 35–62

  40. 40.

    Schöllhorn WI, Nigg BM, Stefanyshyn DJ, et al. Identification of individual walking pattern using time discrete and time continuous data sets. Gait & Posture 2002; 15: 180–6

  41. 41.

    Mateus J. In pursuit of an ecological and fractal approach to soccer coaching. In: Relly T, Cabri J, Araújo D, editors. Science and football V. London: Routledge, 2004: 561–73

  42. 42.

    Schöllhorn WI. Applications of artificial neural nets in clinical biomechanics. Clin Biomechanics 2004; 19: 876–98

  43. 43.

    Hertz J, Krough A, Palmer RG. Introduction to the theory of neural computation. Redwood City (CA): Addison- Wesley, 1991

  44. 44.

    Silva AJ, Costa AM, Oliviera PM, et al. The use of neural network technology to model swimming performance. J Sports Sci Med 2007; 6: 117–25

  45. 45.

    Pfeiffer M, Perl J. Analysis of tactical structures in team handball by means of artificial neural networks. Int J Comput Sci Sport 2006; 5 (1): 4–14

  46. 46.

    Barton G, Lees A, Lisboa P, et al. Visualisation of gait data with Kohonen self-organizing neural maps. Gait & Posture 2006; 24: 46–53

  47. 47.

    Lamb PF. The use of self-organizing maps in analyzing multi-dimensional human movement coordination [PhD thesis]. Dunedin: University of Otago, 2010

  48. 48.

    Perl J. Modeling dynamic systems: basic aspects and application to performance analysis. Int J Comput Sci Sport 2004; 3 (2): 19–28

  49. 49.

    Jaeger H. Short term memory in ‘echo’ state networks. German National Research Institute for Computer Science 2002; GMD-Report No.: 152 [online]. Available from URL: http://www.faculty.iu-bremen.de/hjaeger/pubs/STMEchoStatesTechRep.pdf [Accessed 2011 Sep 20]

  50. 50.

    Williams RJ, Zipser D. (University of California, Institute for Cognitive Science, San Diego). A learning algorithm forcontinually running fully recurrent neural networks: finalreport [report no. 8805]. San Diego (CA): Institute of Cognitive Science, University of California, San Diego, 1988

  51. 51.

    Konen W, Maurer T, von der Malsburg. A fast dynamic link matching algorithm for invariant pattern recognition. Neural Networks 1994; 7: 1019–30

  52. 52.

    Kohonen T. Self-organizing maps. New York: Springer, 1997

  53. 53.

    Perl J, Dauscher P. Dynamic pattern recognition in sport by means of artificial neural networks. In: Begg R, Palaniswami M, editors. Computational intelligence for movement science. Hershey (PA): Idea Group Publishing, 2006: 299–318

  54. 54.

    Lippmann RP. An introduction to computing with neural nets. IEEE ASSP Magazine 1987; 4 (3): 4–22 [online]. Available from URL: http://hawk.cs.csuci.edu/William.Wolfe/UCD/engineering/cse/Graduate/courses/CSC5542/Lippmann.pdf [Accessed 2011 Sep 21]

  55. 55.

    Leondes CT. Algorithm and architectures. San Diego (CA): Academic Press, 1998

  56. 56.

    Perl J, Weber K. A neural network approach to pattern learning in sport. Int J Comput Sci Sport 2004; 3: 67–70

  57. 57.

    Hughes M. Notational analysis: a mathematical perspective. Int J Perform Anal Sport 2004; 4: 97–139

  58. 58.

    Perl J. Game analysis and control by means of continuously learning networks. Int J Perform Anal Sport 2002; 2: 21–35

  59. 59.

    Gruen A. Fundamentals of videogrammetry: a review. Hum Movement Sci 1997; 16: 155–87

  60. 60.

    Passos P, Araújo D, Davids K, et al. Interpersonal dynamics in sport: the role of artificial neural networks and 3-D analysis. Behav Res Meth, 2006; 38 (4): 683–91

  61. 61.

    Memmert D. Can creativity be improved by an attentionbroadening training program? An exploratory study focusing on team sports. Creativity Res J 2007; 19: 281–92

  62. 62.

    Fetz EE, Cheney PD, Mewes K, et al. Control of forelimb activity by populations of corticomotoneuronal and rubromotoneuraonal cells. Progr Brain Res 1989; 80: 437–49

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No sources of funding were used to assist in the preparation of this review. The authors have no conflicts of interest that are directly relevant to the content of this review. The authors would like to thank Gavin Kennedy for his input into the article as part of their research discussion group.

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Correspondence to Mr Aviroop Dutt-Mazumder.

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Dutt-Mazumder, A., Button, C., Robins, A. et al. Neural Network Modelling and Dynamical System Theory. Sports Med 41, 1003–1017 (2011). https://doi.org/10.2165/11593950-000000000-00000

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  • Artificial Neural Network
  • Artificial Neural Network Model
  • Team Sport
  • Dynamical System Theory
  • Artificial Neural Network Architecture